Chapter 1, Problem 5MCCP

WHAT YOU KNOW: We used the rectangular coordinate system to represent ordered pairs of real numbers and to graph equations in two variables. We saw that linear equations can be written in the form $ax+b=0,a\ne 0$, and quadratic equations can be written in the general form $a{x}^2+bx+c=0,a\ne 0$. We solved linear equations. We saw that some equations have no solution, whereas others have all real numbers as solutions. We solved quadratic equations using factoring, the square root property, completing the square, and the quadratic formula. We saw that the discriminant of $a{x}^2+bx+c=0,b^2-4ac$, determines the number and type of solutions. We performed operations with complex numbers and used the imaginary unit $i\left(i=\sqrt{-1},\text{where}{i}^2=-1\right)$ to represent solutions of quadratic equations with negative discriminants. Only real solutions correspond to x-intercepts. We also solved rational equations by multiplying both sides by the least common denominator and clearing fractions. We developed a strategy for solving a variety of applied problems, using equations to model verbal conditions.

In Exercises 1-12, solve each equation.

$4x-2\left(1-x\right)=3\left(2x+1\right)-5$